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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 42, 'aut_gen_orders': [2, 3, 7, 2, 2, 2], 'aut_gens': [[9, 8840280, 16, 11622360, 40723320, 90882840, 136095240], [18, 8840280, 16, 11622360, 40723320, 90882840, 136095240], [9, 12072360, 16, 18240600, 211977360, 40723320, 263265840], [9, 18518400, 16, 11622360, 211977360, 263265840, 302376360], [9, 8840280, 16, 138027000, 40723320, 90882840, 136095240], [9, 203590800, 16, 298454400, 40723320, 90882840, 136095240], [9, 56332200, 16, 44650200, 40723320, 90882840, 136095240]], 'aut_group': '336.210', 'aut_hash': 210, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 336, 'aut_permdeg': 30, 'aut_perms': [8713307294001680552582400, 216411505838306993916459992938833, 254653199716770561281912788160453, 38142904621464457406349390960956, 185524498902352390065992104214729, 212631253409025916000357040504694], 'aut_phi_ratio': 1.75, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 7, 1, 2], [3, 28, 1, 2], [4, 1, 2, 1], [4, 7, 2, 1], [6, 28, 1, 6], [7, 24, 1, 2], [12, 28, 2, 4], [14, 24, 1, 2], [28, 24, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'F_8:C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '168.43', 'autcentquo_hash': 43, 'autcentquo_nilpotent': False, 'autcentquo_order': 168, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_8:C_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 7, 2], [3, 28, 2], [4, 1, 2], [4, 7, 2], [6, 28, 6], [7, 24, 2], [12, 28, 8], [14, 24, 2], [28, 24, 4]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '168.43', 'commutator_count': 1, 'commutator_label': '56.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1049, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['168.43', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 7, 1, 2], [3, 28, 2, 1], [4, 1, 2, 1], [4, 7, 2, 1], [6, 28, 2, 3], [7, 24, 2, 1], [12, 28, 4, 2], [14, 24, 2, 1], [28, 24, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 672, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[7, 0, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.210', 'hash': 1049, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [1, 3, 1, 7, 2, 2, 2], 'inner_gens': [[9, 8840280, 16, 11622360, 40723320, 90882840, 136095240], [9, 8840280, 16, 18240600, 136095240, 263265840, 211977360], [9, 8840280, 16, 11622360, 40723320, 90882840, 136095240], [9, 4515960, 16, 11622360, 167410080, 136095240, 40723320], [9, 203590800, 16, 85367520, 40723320, 90882840, 136095240], [9, 203590800, 16, 298454400, 40723320, 90882840, 136095240], [9, 56332200, 16, 221806920, 40723320, 90882840, 136095240]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': 'F_8:C_3', 'inner_used': [2, 4, 5], 'irrC_degree': 7, 'irrQ_degree': 14, 'irrQ_dim': 14, 'irrR_degree': 14, 'irrep_stats': [[1, 12], [3, 8], [7, 12]], 'label': '672.1049', 'linC_count': 6, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 2, 'linQ_dim': 9, 'linQ_dim_count': 2, 'linR_count': 6, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'F8:C12', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 32, 'number_divisions': 15, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 46, 'number_subgroup_classes': 46, 'number_subgroups': 452, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 56], [4, 16], [6, 168], [7, 48], [12, 224], [14, 48], [28, 96]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[18, 8840280, 16, 11622360, 40723320, 90882840, 136095240]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 1], [6, 2], [7, 2], [12, 1], [14, 3], [28, 1]], 'representations': {'PC': {'code': 324995538681765102188912244406947609597666993724756987018104, 'gens': [1, 2, 5, 6, 7], 'pres': [7, -3, -2, -2, -7, -2, 2, 2, 379, 36, 1136, 58, 675, 14704, 5891, 2468, 515, 14117, 8244, 1783, 1790, 24702, 2757, 4822, 370]}, 'Perm': {'d': 12, 'gens': [9, 8840280, 16, 11622360, 40723320, 90882840, 136095240]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [12], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'F_8:C_{12}', 'transitive_degree': 28, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 144418658
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1049, 'group_order': 672, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 144418669
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1049, 'group_order': 672, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 16, 'size': 1}
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id: 144418680
{'aut_label': '2B', 'centralizer': '7.a1.a1', 'counter': 3, 'group_counter': 1049, 'group_order': 672, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 167410096, 'size': 7}
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id: 144418684
{'aut_label': '2C', 'centralizer': '7.a1.a1', 'counter': 4, 'group_counter': 1049, 'group_order': 672, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 211977360, 'size': 7}
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id: 144418685
{'aut_label': '3A1', 'centralizer': '28.a1.a1', 'counter': 5, 'group_counter': 1049, 'group_order': 672, 'label': '3A1', 'order': 3, 'powers': [6, 1, 5], 'representative': 56332200, 'size': 28}
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id: 144418686
{'aut_label': '3A-1', 'centralizer': '28.a1.a1', 'counter': 6, 'group_counter': 1049, 'group_order': 672, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 6], 'representative': 200768520, 'size': 28}
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id: 144418687
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 1049, 'group_order': 672, 'label': '4A1', 'order': 4, 'powers': [2, 8, 8], 'representative': 18, 'size': 1}
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id: 144418688
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 1049, 'group_order': 672, 'label': '4A-1', 'order': 4, 'powers': [2, 7, 7], 'representative': 9, 'size': 1}
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id: 144418689
{'aut_label': '4B1', 'centralizer': '7.a1.a1', 'counter': 9, 'group_counter': 1049, 'group_order': 672, 'label': '4B1', 'order': 4, 'powers': [2, 10, 10], 'representative': 167410098, 'size': 7}
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id: 144418659
{'aut_label': '4B1', 'centralizer': '7.a1.a1', 'counter': 10, 'group_counter': 1049, 'group_order': 672, 'label': '4B-1', 'order': 4, 'powers': [2, 9, 9], 'representative': 167410089, 'size': 7}
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id: 144418660
{'aut_label': '6A1', 'centralizer': '28.a1.a1', 'counter': 11, 'group_counter': 1049, 'group_order': 672, 'label': '6A1', 'order': 6, 'powers': [5, 3, 11], 'representative': 294110056, 'size': 28}
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id: 144418661
{'aut_label': '6A-1', 'centralizer': '28.a1.a1', 'counter': 12, 'group_counter': 1049, 'group_order': 672, 'label': '6A-1', 'order': 6, 'powers': [6, 3, 12], 'representative': 103225816, 'size': 28}
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id: 144418662
{'aut_label': '6B1', 'centralizer': '28.a1.a1', 'counter': 13, 'group_counter': 1049, 'group_order': 672, 'label': '6B1', 'order': 6, 'powers': [5, 2, 13], 'representative': 123832936, 'size': 28}
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id: 144418663
{'aut_label': '6B-1', 'centralizer': '28.a1.a1', 'counter': 14, 'group_counter': 1049, 'group_order': 672, 'label': '6B-1', 'order': 6, 'powers': [6, 2, 14], 'representative': 203590816, 'size': 28}
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id: 144418664
{'aut_label': '6C1', 'centralizer': '28.a1.a1', 'counter': 15, 'group_counter': 1049, 'group_order': 672, 'label': '6C1', 'order': 6, 'powers': [5, 4, 15], 'representative': 170565240, 'size': 28}
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id: 144418665
{'aut_label': '6C-1', 'centralizer': '28.a1.a1', 'counter': 16, 'group_counter': 1049, 'group_order': 672, 'label': '6C-1', 'order': 6, 'powers': [6, 4, 16], 'representative': 88947360, 'size': 28}
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id: 144418666
{'aut_label': '7A1', 'centralizer': '24.a1.a1', 'counter': 17, 'group_counter': 1049, 'group_order': 672, 'label': '7A1', 'order': 7, 'powers': [17, 18, 1], 'representative': 8388000, 'size': 24}
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id: 144418667
{'aut_label': '7A-1', 'centralizer': '24.a1.a1', 'counter': 18, 'group_counter': 1049, 'group_order': 672, 'label': '7A-1', 'order': 7, 'powers': [18, 17, 1], 'representative': 11622360, 'size': 24}
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id: 144418668
{'aut_label': '12A1', 'centralizer': '28.a1.a1', 'counter': 19, 'group_counter': 1049, 'group_order': 672, 'label': '12A1', 'order': 12, 'powers': [13, 9, 22], 'representative': 287130249, 'size': 28}
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id: 144418670
{'aut_label': '12A-1', 'centralizer': '28.a1.a1', 'counter': 20, 'group_counter': 1049, 'group_order': 672, 'label': '12A-1', 'order': 12, 'powers': [14, 10, 21], 'representative': 247288458, 'size': 28}
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id: 144418671
{'aut_label': '12A-1', 'centralizer': '28.a1.a1', 'counter': 21, 'group_counter': 1049, 'group_order': 672, 'label': '12A5', 'order': 12, 'powers': [14, 9, 20], 'representative': 247288449, 'size': 28}
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id: 144418672
{'aut_label': '12A1', 'centralizer': '28.a1.a1', 'counter': 22, 'group_counter': 1049, 'group_order': 672, 'label': '12A-5', 'order': 12, 'powers': [13, 10, 19], 'representative': 287130258, 'size': 28}
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id: 144418673
{'aut_label': '12B1', 'centralizer': '28.a1.a1', 'counter': 23, 'group_counter': 1049, 'group_order': 672, 'label': '12B1', 'order': 12, 'powers': [13, 7, 26], 'representative': 248584449, 'size': 28}
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id: 144418674
{'aut_label': '12B-1', 'centralizer': '28.a1.a1', 'counter': 24, 'group_counter': 1049, 'group_order': 672, 'label': '12B-1', 'order': 12, 'powers': [14, 8, 25], 'representative': 142058898, 'size': 28}
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id: 144418675
{'aut_label': '12B-1', 'centralizer': '28.a1.a1', 'counter': 25, 'group_counter': 1049, 'group_order': 672, 'label': '12B5', 'order': 12, 'powers': [14, 7, 24], 'representative': 142058889, 'size': 28}
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id: 144418676
{'aut_label': '12B1', 'centralizer': '28.a1.a1', 'counter': 26, 'group_counter': 1049, 'group_order': 672, 'label': '12B-5', 'order': 12, 'powers': [13, 8, 23], 'representative': 248584458, 'size': 28}
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id: 144418677
{'aut_label': '14A1', 'centralizer': '24.a1.a1', 'counter': 27, 'group_counter': 1049, 'group_order': 672, 'label': '14A1', 'order': 14, 'powers': [17, 28, 2], 'representative': 23037856, 'size': 24}
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id: 144418678
{'aut_label': '14A-1', 'centralizer': '24.a1.a1', 'counter': 28, 'group_counter': 1049, 'group_order': 672, 'label': '14A-1', 'order': 14, 'powers': [18, 27, 2], 'representative': 16134616, 'size': 24}
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id: 144418679
{'aut_label': '28A1', 'centralizer': '24.a1.a1', 'counter': 29, 'group_counter': 1049, 'group_order': 672, 'label': '28A1', 'order': 28, 'powers': [27, 30, 7], 'representative': 5570649, 'size': 24}
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id: 144418681
{'aut_label': '28A-1', 'centralizer': '24.a1.a1', 'counter': 30, 'group_counter': 1049, 'group_order': 672, 'label': '28A-1', 'order': 28, 'powers': [28, 29, 8], 'representative': 11622378, 'size': 24}
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id: 144418682
{'aut_label': '28A-1', 'centralizer': '24.a1.a1', 'counter': 31, 'group_counter': 1049, 'group_order': 672, 'label': '28A5', 'order': 28, 'powers': [28, 32, 7], 'representative': 11622369, 'size': 24}
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id: 144418683
{'aut_label': '28A1', 'centralizer': '24.a1.a1', 'counter': 32, 'group_counter': 1049, 'group_order': 672, 'label': '28A-5', 'order': 28, 'powers': [27, 31, 8], 'representative': 5570658, 'size': 24}
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gps_qchar • Show schema
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id: 14057141
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 14057148
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
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id: 14057149
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
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id: 14057150
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.1d', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057151
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.1e', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, -2, -2, -2, -2], 'schur_index': 1}
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id: 14057152
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.1f', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057153
{'cdim': 3, 'counter': 7, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.3a', 'multiplicity': 2, 'nt': [7, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
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id: 14057154
{'cdim': 3, 'counter': 8, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.3b', 'multiplicity': 2, 'nt': [14, 5], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
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id: 14057142
{'cdim': 7, 'counter': 10, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.7a', 'multiplicity': 1, 'nt': [8, 36], 'qdim': 7, 'qvalues': [7, 7, -1, -1, 1, 1, 7, 7, -1, -1, -1, -1, 1, 1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057143
{'cdim': 7, 'counter': 11, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.7b', 'multiplicity': 1, 'nt': [14, 18], 'qdim': 7, 'qvalues': [7, 7, -1, -1, 1, 1, -7, -7, 1, 1, -1, -1, 1, 1, -1, -1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057155
{'cdim': 3, 'counter': 9, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.3c', 'multiplicity': 4, 'nt': [28, 13], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057144
{'cdim': 7, 'counter': 12, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.7c', 'multiplicity': 2, 'nt': [24, 283], 'qdim': 14, 'qvalues': [14, 14, -2, -2, -1, -1, 14, 14, -2, -2, 1, 1, -1, -1, 1, 1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057145
{'cdim': 7, 'counter': 13, 'faithful': True, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.7d', 'multiplicity': 2, 'nt': [28, 79], 'qdim': 14, 'qvalues': [14, -14, 2, -2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057146
{'cdim': 7, 'counter': 14, 'faithful': False, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.7e', 'multiplicity': 2, 'nt': [42, 67], 'qdim': 14, 'qvalues': [14, 14, -2, -2, -1, -1, -14, -14, 2, 2, 1, 1, -1, -1, 1, 1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 14057147
{'cdim': 7, 'counter': 15, 'faithful': True, 'group': '672.1049', 'group_order': 672, 'image': None, 'label': '672.1049.7f', 'multiplicity': 4, 'nt': [84, 0], 'qdim': 28, 'qvalues': [28, -28, 4, -4, -2, -2, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 33407878
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 672, 'label': '672.1049.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 33407889
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 336, 'label': '672.1049.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 33407900
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 224, 'label': '672.1049.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 33407904
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 224, 'label': '672.1049.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
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id: 33407905
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 168, 'label': '672.1049.1d1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
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id: 33407906
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 168, 'label': '672.1049.1d2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
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id: 33407907
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 112, 'label': '672.1049.1e1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 33407908
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 112, 'label': '672.1049.1e2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
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id: 33407909
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 9, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 56, 'label': '672.1049.1f1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]]]}
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id: 33407879
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 10, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 56, 'label': '672.1049.1f2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]]]}
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id: 33407880
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 11, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 56, 'label': '672.1049.1f3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]]]}
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id: 33407881
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 672, 'counter': 12, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 56, 'label': '672.1049.1f4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[-1, 0]], [[-1, 0]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]]]}
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id: 33407882
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1.a1', 'kernel_order': 32, 'label': '672.1049.3a1', 'nt': [7, 3], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]]]}
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id: 33407883
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '21.1', 'image_order': 21, 'indicator': 0, 'kernel': '21.a1.a1', 'kernel_order': 32, 'label': '672.1049.3a2', 'nt': [7, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]]]}
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id: 33407884
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.a1', 'kernel_order': 16, 'label': '672.1049.3b1', 'nt': [14, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]]]}
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id: 33407885
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 7, 'dim': 3, 'faithful': False, 'field': [2, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '42.2', 'image_order': 42, 'indicator': 0, 'kernel': '42.a1.a1', 'kernel_order': 16, 'label': '672.1049.3b2', 'nt': [14, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 2], [1, -3]], [[-1, 0], [-1, 1], [-1, 2], [-1, -3]], [[-1, 1], [-1, 2], [-1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[1, 0], [1, 1], [1, 2], [1, -3]], [[-1, 1], [-1, 2], [-1, -3]]]}
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id: 33407886
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 28, 'dim': 3, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '84.2', 'image_order': 84, 'indicator': 0, 'kernel': '84.a1.a1', 'kernel_order': 8, 'label': '672.1049.3c1', 'nt': [28, 13], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 7]], [[3, 7]], [[-3, 7]], [[3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [-1, 4], [-1, 8]], [[-1, 2], [1, 4], [1, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 2], [1, 4], [1, 8]], [[1, 2], [-1, 4], [-1, 8]], [[1, 1], [-1, 7], [1, 9], [-1, 11]], [[1, 1], [1, 9], [-1, 11]], [[-1, 1], [-1, 9], [1, 11]], [[-1, 1], [1, 7], [-1, 9], [1, 11]]]}
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id: 33407887
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 28, 'dim': 3, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '84.2', 'image_order': 84, 'indicator': 0, 'kernel': '84.a1.a1', 'kernel_order': 8, 'label': '672.1049.3c2', 'nt': [28, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 7]], [[-3, 7]], [[3, 7]], [[-3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, 4], [1, 8]], [[-1, 0], [1, 2], [-1, 4], [-1, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [-1, 4], [-1, 8]], [[1, 0], [-1, 2], [1, 4], [1, 8]], [[1, 1], [1, 9], [-1, 11]], [[1, 1], [-1, 7], [1, 9], [-1, 11]], [[-1, 1], [1, 7], [-1, 9], [1, 11]], [[-1, 1], [-1, 9], [1, 11]]]}
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id: 33407888
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 28, 'dim': 3, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '84.2', 'image_order': 84, 'indicator': 0, 'kernel': '84.a1.a1', 'kernel_order': 8, 'label': '672.1049.3c3', 'nt': [28, 13], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 7]], [[3, 7]], [[-3, 7]], [[3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [1, 4], [1, 8]], [[-1, 0], [1, 2], [-1, 4], [-1, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [-1, 4], [-1, 8]], [[1, 0], [-1, 2], [1, 4], [1, 8]], [[-1, 1], [-1, 9], [1, 11]], [[-1, 1], [1, 7], [-1, 9], [1, 11]], [[1, 1], [-1, 7], [1, 9], [-1, 11]], [[1, 1], [1, 9], [-1, 11]]]}
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id: 33407890
{'center': '21.a1.a1', 'center_index': 21, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 28, 'dim': 3, 'faithful': False, 'field': [4, 0, -3, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '84.2', 'image_order': 84, 'indicator': 0, 'kernel': '84.a1.a1', 'kernel_order': 8, 'label': '672.1049.3c4', 'nt': [28, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 7]], [[-3, 7]], [[3, 7]], [[-3, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 2], [-1, 4], [-1, 8]], [[-1, 2], [1, 4], [1, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 2], [1, 4], [1, 8]], [[1, 2], [-1, 4], [-1, 8]], [[-1, 1], [1, 7], [-1, 9], [1, 11]], [[-1, 1], [-1, 9], [1, 11]], [[1, 1], [1, 9], [-1, 11]], [[1, 1], [-1, 7], [1, 9], [-1, 11]]]}
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id: 33407891
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '168.43', 'image_order': 168, 'indicator': 1, 'kernel': '168.a1.a1', 'kernel_order': 4, 'label': '672.1049.7a', 'nt': [8, 36], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407892
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 1, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.1049.7b', 'nt': [14, 18], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407893
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '168.43', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1.a1', 'kernel_order': 4, 'label': '672.1049.7c1', 'nt': [24, 283], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407894
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '168.43', 'image_order': 168, 'indicator': 0, 'kernel': '168.a1.a1', 'kernel_order': 4, 'label': '672.1049.7c2', 'nt': [24, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407895
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 4, 'dim': 7, 'faithful': True, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '672.1049', 'image_order': 672, 'indicator': 0, 'kernel': '672.a1.a1', 'kernel_order': 1, 'label': '672.1049.7d1', 'nt': [28, 79], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-7, 1]], [[7, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407896
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 4, 'dim': 7, 'faithful': True, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '672.1049', 'image_order': 672, 'indicator': 0, 'kernel': '672.a1.a1', 'kernel_order': 1, 'label': '672.1049.7d2', 'nt': [28, 2], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[7, 1]], [[-7, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407897
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 27, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.1049.7e1', 'nt': [42, 67], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407898
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 28, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '336.210', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 2, 'label': '672.1049.7e2', 'nt': [42, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[-7, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407899
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 29, 'cyclotomic_n': 12, 'dim': 7, 'faithful': True, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '672.1049', 'image_order': 672, 'indicator': 0, 'kernel': '672.a1.a1', 'kernel_order': 1, 'label': '672.1049.7f1', 'nt': [84, 0], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[-7, 3]], [[7, 3]], [[1, 3]], [[-1, 3]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407901
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 30, 'cyclotomic_n': 12, 'dim': 7, 'faithful': True, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '672.1049', 'image_order': 672, 'indicator': 0, 'kernel': '672.a1.a1', 'kernel_order': 1, 'label': '672.1049.7f2', 'nt': [84, 4], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[7, 3]], [[-7, 3]], [[-1, 3]], [[1, 3]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407902
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 31, 'cyclotomic_n': 12, 'dim': 7, 'faithful': True, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '672.1049', 'image_order': 672, 'indicator': 0, 'kernel': '672.a1.a1', 'kernel_order': 1, 'label': '672.1049.7f3', 'nt': [84, 0], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[7, 3]], [[-7, 3]], [[-1, 3]], [[1, 3]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[-1, 5]], [[1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 33407903
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 4, 'counter': 32, 'cyclotomic_n': 12, 'dim': 7, 'faithful': True, 'field': [1, 0, 1], 'group': '672.1049', 'group_counter': 1049, 'group_order': 672, 'image': None, 'image_isoclass': '672.1049', 'image_order': 672, 'indicator': 0, 'kernel': '672.a1.a1', 'kernel_order': 1, 'label': '672.1049.7f4', 'nt': [84, 4], 'q_character': None, 'values': [[[7, 0]], [[-7, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[-7, 3]], [[7, 3]], [[1, 3]], [[-1, 3]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 5]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 116054876
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '672.1049.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1049', 'subgroup_hash': 1049, 'subgroup_order': 672, 'subgroup_tex': 'F_8:C_{12}', 'supersolvable': False, 'sylow': 0}
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id: 116054887
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1049.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
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id: 116054898
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 224, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 14, 'label': '672.1049.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.173', 'subgroup_hash': 173, 'subgroup_order': 224, 'subgroup_tex': 'C_4\\times F_8', 'supersolvable': False, 'sylow': 0}
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id: 116054909
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': True, 'core_order': 168, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1049.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.43', 'subgroup_hash': 43, 'subgroup_order': 168, 'subgroup_tex': 'F_8:C_3', 'supersolvable': False, 'sylow': 0}
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id: 116054917
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 112, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1049.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
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id: 116054918
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '672.1049.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
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id: 116054919
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.8.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.2', 'subgroup_hash': 2, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 116054920
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 56, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1049.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.11', 'subgroup_hash': 11, 'subgroup_order': 56, 'subgroup_tex': 'F_8', 'supersolvable': False, 'sylow': 0}
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id: 116054921
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 116054877
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 116054878
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 116054879
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
-
id: 116054880
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '672.1049.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '21.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 21, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 2}
-
id: 116054881
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 116054882
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 116054883
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
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id: 116054884
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 116054885
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 116054886
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 21, 'label': '672.1049.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
-
id: 116054888
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1049.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '42.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_6', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 116054889
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 116054890
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 116054891
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 116054892
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 116054893
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 116054894
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 116054895
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 116054896
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1049.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 116054897
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 116054899
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
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id: 116054900
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 116054901
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 116054902
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '672.1049.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
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id: 116054903
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 116054904
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 116054905
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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id: 116054906
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 4, 'counter': 37, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '672.1049.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.43', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 116054907
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 116054908
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 116054910
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 116054911
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1049.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 116054912
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '672.1049.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
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id: 116054913
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1049.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.210', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 210, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 116054914
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 116054915
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1049.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 116054916
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1049', 'ambient_counter': 1049, 'ambient_order': 672, 'ambient_tex': 'F_8:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 1, 'counter': 46, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '672.1049.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '672.1049', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1049, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 116054876
{'ambient': '672.1049', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.a1.a1', 'complements': ['672.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '7.a1.a1', '8.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7909, 6497, 8079, 6877, 5051, 4534, 5051, 4534], 'generators': [8388000, 167410080, 40723320, 136095240, 9, 16, 8840280], 'label': '672.1049.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
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id: 116054877
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 14, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1'], 'contains': ['28.b1.a1', '42.c1.a1', '56.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7359, -1, 6355, -1, 7121, -1, 7121, -1], 'generators': [40723320, 167410089, 136095240, 16, 8840280], 'label': '672.1049.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 116054878
{'ambient': '672.1049', 'aut_centralizer_order': 4, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 28, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.c1.a1', '28.d1.a1', '42.a1.a1', '56.a1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3446, -1, 3513, -1, 4146, -1, 4146, -1], 'generators': [167410080, 40723320, 136095240, 16, 8840280], 'label': '672.1049.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 116054879
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '8.a1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '112.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5072, -1, 4967, -1, 1887, -1, 1887, -1], 'generators': [8388000, 16, 8840280], 'label': '672.1049.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
-
id: 116054880
{'ambient': '672.1049', 'aut_centralizer_order': 8, 'aut_label': '21.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '42.2', 'aut_weyl_index': 8, 'centralizer': '21.a1.a1', 'complements': ['32.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1'], 'core': '21.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6426, 8504, 6961, 8510, 6010, 8096, 6010, 8096], 'generators': [167410080, 40723320, 136095240, 9, 16], 'label': '672.1049.21.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '21.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['42.a1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '168.43', 'quotient_action_image': '21.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
-
id: 116054881
{'ambient': '672.1049', 'aut_centralizer_order': 7, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 56, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '8.a1.a1'], 'contains': ['48.a1.a1', '168.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9579, -1, 8970, -1, 5074, -1, 5074, -1], 'generators': [8388000, 9, 16], 'label': '672.1049.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054882
{'ambient': '672.1049', 'aut_centralizer_order': 6, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1', '84.b1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [9504, -1, 9065, -1, 9448, -1, 9448, -1], 'generators': [167410080, 9, 16, 8840280], 'label': '672.1049.28.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054883
{'ambient': '672.1049', 'aut_centralizer_order': 4, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 28, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '14.b1.a1', '14.c1.a1'], 'contains': ['56.d1.a1', '84.d1.a1', '112.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5365, -1, 5237, -1, 5630, -1, 5630, -1], 'generators': [40723320, 136095240, 16, 8840280], 'label': '672.1049.28.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 116054884
{'ambient': '672.1049', 'aut_centralizer_order': 4, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 28, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1'], 'contains': ['56.d1.a1', '84.e1.a1', '112.b1.a1'], 'core': '672.a1.a1', 'coset_action_label': '28T79', 'count': 7, 'diagramx': [2505, -1, 2477, -1, 3393, -1, 3393, -1], 'generators': [40723320, 167410096, 136095240, 8840280], 'label': '672.1049.28.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 116054885
{'ambient': '672.1049', 'aut_centralizer_order': 4, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 28, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.c1.a1'], 'contains': ['56.d1.a1', '84.a1.a1', '112.c1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1174, -1, 1154, -1, 2366, -1, 2366, -1], 'generators': [167410080, 40723320, 136095240, 8840280], 'label': '672.1049.28.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 116054886
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '16.a1.a1'], 'contains': ['96.a1.a1', '224.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': '32T34615', 'count': 8, 'diagramx': [414, -1, 401, -1, 281, -1, 281, -1], 'generators': [8388000, 8840280], 'label': '672.1049.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
-
id: 116054887
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 2, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '14.c1.a1', '16.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3996, 3996, 3594, 4021, 3035, 2479, 3035, 2479], 'generators': [8388000, 167410080, 40723320, 136095240, 16, 8840280], 'label': '672.1049.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
-
id: 116054888
{'ambient': '672.1049', 'aut_centralizer_order': 16, 'aut_label': '42.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '21.1', 'aut_weyl_index': 16, 'centralizer': '21.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.d1.a1', '84.e1.a1'], 'core': '42.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3394, 5554, 3273, 5571, 4511, 5986, 4511, 5986], 'generators': [167410080, 40723320, 136095240, 16], 'label': '672.1049.42.a1.a1', 'mobius_quo': 1, 'mobius_sub': -7, 'normal_closure': '42.a1.a1', 'normal_contained_in': ['6.a1.a1', '21.a1.a1'], 'normal_contains': ['84.a1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '336.210', 'quotient_action_image': '21.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
-
id: 116054889
{'ambient': '672.1049', 'aut_centralizer_order': 8, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.2', 'aut_weyl_index': 56, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.a1', '84.d1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8232, -1, 7794, -1, 7934, -1, 7934, -1], 'generators': [167410080, 40723320, 9, 16], 'label': '672.1049.42.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054890
{'ambient': '672.1049', 'aut_centralizer_order': 8, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '6.2', 'aut_weyl_index': 56, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.d1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6758, -1, 6648, -1, 6740, -1, 6740, -1], 'generators': [167410080, 40723320, 136095249, 16], 'label': '672.1049.42.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054891
{'ambient': '672.1049', 'aut_centralizer_order': 14, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '3.1', 'aut_weyl_index': 112, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '16.a1.a1', '24.a1.a1'], 'contains': ['96.a1.a1', '336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4116, -1, 4083, -1, 1514, -1, 1514, -1], 'generators': [8388000, 16], 'label': '672.1049.48.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054892
{'ambient': '672.1049', 'aut_centralizer_order': 12, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1', '28.a1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.b1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5365, -1, 5099, -1, 5576, -1, 5584, -1], 'generators': [167410080, 16, 8840280], 'label': '672.1049.56.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054893
{'ambient': '672.1049', 'aut_centralizer_order': 6, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '14.a1.a1', '28.a1.a1'], 'contains': ['112.a1.a1', '168.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [9783, -1, 9803, -1, 9456, -1, 9464, -1], 'generators': [9, 16, 8840280], 'label': '672.1049.56.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054894
{'ambient': '672.1049', 'aut_centralizer_order': 6, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1', '28.a1.a1'], 'contains': ['112.a1.a1', '168.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8367, -1, 8291, -1, 7752, -1, 7760, -1], 'generators': [167410089, 16, 8840280], 'label': '672.1049.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054895
{'ambient': '672.1049', 'aut_centralizer_order': 4, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '12.3', 'aut_weyl_index': 28, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1.a1', '28.c1.a1', '28.d1.a1'], 'contains': ['168.e1.a1', '224.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2461, -1, 2389, -1, 2959, -1, 2967, -1], 'generators': [40723320, 136095240, 8840280], 'label': '672.1049.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.d1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 116054896
{'ambient': '672.1049', 'aut_centralizer_order': 16, 'aut_label': '84.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '21.1', 'aut_weyl_index': 16, 'centralizer': '21.a1.a1', 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.d1.a1', '42.a1.a1'], 'contains': ['168.e1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1535, 3135, 1446, 3163, 2374, 4918, 2381, 4918], 'generators': [167410080, 40723320, 136095240], 'label': '672.1049.84.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.a1.a1', '42.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': '21.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
-
id: 116054897
{'ambient': '672.1049', 'aut_centralizer_order': 24, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '42.b1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [9128, -1, 8964, -1, 8604, -1, 8611, -1], 'generators': [167410080, 9, 16], 'label': '672.1049.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054898
{'ambient': '672.1049', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '336.210', 'aut_weyl_index': 1, 'centralizer': '168.a1.a1', 'complements': ['224.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '21.a1.a1', '24.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6780, 8177, 6648, 8184, 5630, 6617, 5630, 6617], 'generators': [8388000, 167410080, 40723320, 136095240, 9, 16], 'label': '672.1049.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '21.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '168.43', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
-
id: 116054899
{'ambient': '672.1049', 'aut_centralizer_order': 8, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.b1.a1', '42.c1.a1'], 'contains': ['168.b1.a1', '168.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7532, -1, 6925, -1, 6900, -1, 6907, -1], 'generators': [167410080, 40723329, 16], 'label': '672.1049.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.c1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054900
{'ambient': '672.1049', 'aut_centralizer_order': 16, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 112, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.b1.a1', '168.d1.a1', '168.e1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4109, -1, 3783, -1, 4747, -1, 4755, -1], 'generators': [167410080, 40723320, 16], 'label': '672.1049.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.d1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054901
{'ambient': '672.1049', 'aut_centralizer_order': 16, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 112, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '42.a1.a1'], 'contains': ['168.d1.a1', '168.e1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3191, -1, 2908, -1, 3834, -1, 3842, -1], 'generators': [167410080, 40723320, 136095256], 'label': '672.1049.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054902
{'ambient': '672.1049', 'aut_centralizer_order': 14, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '3.1', 'aut_weyl_index': 112, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '32.a1.a1', '48.a1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [203, -1, 197, -1, 1065, -1, 1057, -1], 'generators': [8388000], 'label': '672.1049.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054903
{'ambient': '672.1049', 'aut_centralizer_order': 12, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '28.b1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1'], 'contains': ['224.a1.a1', '336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [6306, -1, 5610, -1, 5226, -1, 5234, -1], 'generators': [16, 8840280], 'label': '672.1049.112.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054904
{'ambient': '672.1049', 'aut_centralizer_order': 12, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '56.a1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4748, -1, 4222, -1, 3918, -1, 3925, -1], 'generators': [167410096, 8840280], 'label': '672.1049.112.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054905
{'ambient': '672.1049', 'aut_centralizer_order': 12, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.d1.a1', '56.a1.a1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2204, -1, 3418, -1, 2457, -1, 2465, -1], 'generators': [167410080, 8840280], 'label': '672.1049.112.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.c1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054906
{'ambient': '672.1049', 'aut_centralizer_order': 168, 'aut_label': '168.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '1.a1.a1', 'complements': ['4.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.b1.a1', '84.b1.a1'], 'contains': ['336.a1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9601, 8095, 9503, 8102, 9030, 8096, 9038, 8096], 'generators': [9, 16], 'label': '672.1049.168.a1.a1', 'mobius_quo': 0, 'mobius_sub': -56, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['21.a1.a1'], 'normal_contains': ['336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '168.43', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.43', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054907
{'ambient': '672.1049', 'aut_centralizer_order': 48, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '84.b1.a1', '84.c1.a1', '84.d1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5448, -1, 5194, -1, 5812, -1, 5820, -1], 'generators': [167410080, 16], 'label': '672.1049.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054908
{'ambient': '672.1049', 'aut_centralizer_order': 24, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '2.1', 'aut_weyl_index': 168, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '84.b1.a1', '84.c1.a1'], 'contains': ['336.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8406, -1, 8116, -1, 7326, -1, 7334, -1], 'generators': [167410089, 16], 'label': '672.1049.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '21.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.c1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054909
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 2, 'centralizer': '168.a1.a1', 'complements': ['168.a1.a1', '168.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1', '28.d1.a1', '32.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1046, 1496, 1235, 1490, 905, 1000, 905, 1000], 'generators': [8388000, 167410080, 40723320, 136095240, 8840280], 'label': '672.1049.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
-
id: 116054910
{'ambient': '672.1049', 'aut_centralizer_order': 16, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.d1.a1', '84.e1.a1'], 'contains': ['336.b1.a1', '336.c1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4101, -1, 4317, -1, 4504, -1, 4511, -1], 'generators': [167410080, 40723336], 'label': '672.1049.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.d1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054911
{'ambient': '672.1049', 'aut_centralizer_order': 16, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 112, 'centralizer': '21.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '84.a1.a1', '84.d1.a1', '84.e1.a1'], 'contains': ['336.c1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3191, -1, 2608, -1, 3332, -1, 3340, -1], 'generators': [167410080, 40723320], 'label': '672.1049.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.e1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 116054912
{'ambient': '672.1049', 'aut_centralizer_order': 12, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '28.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '56.d1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2235, -1, 2922, -1, 2625, -1, 2632, -1], 'generators': [8840280], 'label': '672.1049.224.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054913
{'ambient': '672.1049', 'aut_centralizer_order': 336, 'aut_label': '336.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.b1.a1', '168.c1.a1'], 'contains': ['672.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7427, 5595, 5844, 5613, 5515, 7027, 5523, 7027], 'generators': [16], 'label': '672.1049.336.a1.a1', 'mobius_quo': -1, 'mobius_sub': 56, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['42.a1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '336.210', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.210', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054914
{'ambient': '672.1049', 'aut_centralizer_order': 48, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '168.b1.a1', '168.d1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4402, -1, 4602, -1, 4207, -1, 4214, -1], 'generators': [167410096], 'label': '672.1049.336.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '42.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 116054915
{'ambient': '672.1049', 'aut_centralizer_order': 48, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 336, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '168.b1.a1', '168.d1.a1', '168.e1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3409, -1, 3740, -1, 3347, -1, 3355, -1], 'generators': [167410080], 'label': '672.1049.336.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '336.c1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 116054916
{'ambient': '672.1049', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1'], 'contains': [], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3409, 4447, 3740, 4470, 3347, 5959, 3355, 5959], 'generators': [], 'label': '672.1049.672.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['84.a1.a1', '336.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 116054917
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 2, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '42.a1.a1', '48.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3341, 4612, 2959, 4634, 3035, 4096, 3035, 4096], 'generators': [8388000, 167410080, 40723320, 136095240, 16], 'label': '672.1049.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '42.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '336.210', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
-
id: 116054918
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 14, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '21.a1.a1', '28.a1.a1'], 'core': '21.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8375, -1, 7013, -1, 7029, -1, 7029, -1], 'generators': [167410080, 40723320, 136095240, 9, 16, 8840280], 'label': '672.1049.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
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id: 116054919
{'ambient': '672.1049', 'aut_centralizer_order': 1, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '42.2', 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '56.b1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9797, -1, 8685, -1, 4481, -1, 4481, -1], 'generators': [8388000, 9, 16, 8840280], 'label': '672.1049.8.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
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id: 116054920
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 2, 'centralizer': '168.a1.a1', 'complements': ['56.b1.a1', '56.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['84.a1.a1', '96.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1791, 2233, 1709, 2265, 905, 3877, 905, 3877], 'generators': [8388000, 167410080, 40723320, 136095240], 'label': '672.1049.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '672.1049', 'quotient_action_image': '3.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
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id: 116054921
{'ambient': '672.1049', 'aut_centralizer_order': 2, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 14, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1'], 'contains': ['28.b1.a1', '42.b1.a1', '56.b1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8375, -1, 7816, -1, 8148, -1, 8148, -1], 'generators': [40723320, 136095240, 9, 16, 8840280], 'label': '672.1049.14.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '168.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
